arXiv subjects
Publications and source records attributed to R. A. Bertlmann.
I want to give an impression of the time I spent together with John S. Bell, of the atmosphere of our collaboration and friendship. I briefly review our work, the methods of nonrelativistic approximations to quantum field theory for calculating the properties of heavy quark-antiquark bound states.
Investigation at a $ϕ$--factory can shed light on several debated issues in particle physics. We discuss: i) recent theoretical development and experimental progress in kaon physics relevant for the Standard Model tests in the flavor sector, ii) the sensitivity we can reach in probing CPT and Quantum Mechanics from time evolution of entangled kaon states, iii) the interest for improving on the present measurements of non-leptonic and radiative decays of kaons and eta/eta$^\prime$ mesons, iv) the contribution to understand the nature of light scalar mesons, and v) the opportunity to search for narrow di-lepton resonances suggested by recent models proposing a hidden dark-matter sector. We also report on the $e^+ e^-$ physics in the continuum with the measurements of (multi)hadronic cross sections and the study of gamma gamma processes.
Geometric phase phenomena in single neutrons have been observed in polarimeter and interferometer experiments. Interacting with static and time dependent magnetic fields, the state vectors acquire a geometric phase tied to the evolution within spin subspace. In a polarimeter experiment the non-additivity of quantum phases for mixed spin input states is observed. In a Si perfect-crystal interferometer experiment appearance of geometric phases, induced by interaction with an oscillating magnetic field, is verified. The total system is characterized by an entangled state, consisting of neutron and radiation fields, governed by a Jaynes-Cummings Hamiltonian. In addition, the influence of the geometric phase on a Bell measurement, expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, is studied. It is demonstrated that the effect of geometric phase can be balanced by an appropriate change of Bell angles.
The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. in [Phys. Rev. A 69, 032112 (2004)], and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time dependent interaction with two radio-frequency (rf) fields. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme, yields a sinusoidal oscillation of the correlation function S, dependent on the geometric phase, such that it varies in the range between 2 and 2\sqrt{2} and, therefore, always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like-CHSH inequality, where S remains 2\sqrt2 for all settings of the geometric phase.
Relevant aspects for testing Bell inequalities with entangled meson-antimeson systems are analyzed. In particular, we argue that the result of A. Go, J. Mod. Optics 51, 991 (2004), which nicely illustrate the quantum entanglement of B-meson pairs, cannot be considered as a Bell-test refuting local realism.
We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators and show that the entanglement witness which shows the maximal violation of a generalized Bell inequality (GBI) is a tangent functional to the convex set S subset H_s of separable states. This violation equals the euclidean distance in H_s of the entangled state to S and thus entanglement, GBI and tangent functional are only different aspects of the same geometric picture. This is explicitly illustrated in the example of two spins, where also a comparison with familiar Bell inequalities is presented.
We consider the time evolution of the density matrix $ρ$ in a 2-dimensional complex Hilbert space. We allow for dissipation by adding to the von Neumann equation a term $D[ρ]$, which is of Lindblad type in order to assure complete positivity of the time evolution. We present five equivalent forms of $D[ρ]$. In particular, we connect the familiar dissipation matrix $L$ with a geometric version of $D[ρ]$, where $L$ consists of a positive sum of projectors onto planes in $\mathbf{R}^3$. We also study the minimal number of Lindblad terms needed to describe the most general case of $D[ρ]$. All proofs are worked out comprehensively, as they present at the same time a practical procedure how to determine explicitly the different forms of $D[ρ]$. Finally, we perform a general discussion of the asymptotic behaviour $t \to \infty$ of the density matrix and we relate the two types of asymptotic behaviour with our geometric version of $D[ρ]$.
For the entangled neutral kaon system we formulate a Bell inequality sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound on the leptonic CP asymmetry which is violated by experimental data. Furthermore, we connect the Bell inequality with a decoherence approach and find a lower bound on the decoherence parameter which practically corresponds to Furry's hypothesis.
We give an introduction to an entangled massive system, specifically the neutral kaon system, which has similarities to the entangled two photon system, but, however, also challenging differences.
In the context of the entangled $B^0 \bar B^0$ state produced at the $Υ(4S)$ resonance, we consider a modification of the usual quantum-mechanical time evolution with a dissipative term, which contains only one parameter denoted by $λ$ and respects complete positivity. In this way a decoherence effect is introduced in the time evolution of the 2-particle $B^0 \bar B^0$ state, which becomes stronger with increasing distance between the two particles. While our model of time evolution has decoherence for the 2-particle system, we assume that, after the decay of one of the two B mesons, the resulting 1-particle state obeys the purely quantum-mechanical time evolution. From the data on dilepton events we derive an upper bound on $λ$. We also show how $λ$ is related to the so-called ``decoherence parameter'' $ζ$, which parameterizes decoherence in neutral flavoured meson--antimeson systems.
We are dealing with two-dimensional gravitational anomalies, specifically with the Einstein anomaly and the Weyl anomaly, and we show that they are fully determined by dispersion relations independent of any renormalization procedure (or ultraviolet regularization). The origin of the anomalies is the existence of a superconvergence sum rule for the imaginary part of the relevant formfactor. In the zero mass limit the imaginary part of the formfactor approaches a $δ$-function singularity at zero momentum squared, exhibiting in this way the infrared feature of the gravitational anomalies. We find an equivalence between the dispersive approach and the dimensional regularization procedure. The Schwinger terms appearing in the equal time commutators of the energy momentum tensors can be calculated by the same dispersive method. Although all computations are performed in two dimensions the method is expected to work in higher dimensions too.
We evaluate the gravitational Schwinger terms for the specific two-dimensional model of Weyl fermions in a gravitational background field using a technique introduced by Kallen and find a relation which connects the Schwinger terms with the linearized gravitational anomalies.
The gravitational anomalies in two dimensions, specifically the Einstein anomaly and the Weyl anomaly, are fully determined by means of dispersion relations. In this approach the anomalies originate from the peculiar infrared feature of the imaginary part of the relevant formfactor which approaches a $δ$-function singularity at zero momentum squared when $m \to 0$.
We consider strangeness correlations of the EPR type in K^0 \bar{K}^0 pairs created in a J^{PC} = 1^{--} state as a function of time under the hypothesis that spontaneous decoherence takes place. We parameterize the degree of decoherence by a factor (1-ζ) which multiplies the quantum-mechanical interference terms occurring in the amplitudes for like and unlike strangeness events and discuss the dependence of this procedure on the basis chosen in the K^0--\bar{K}^0 space to which the interference terms correspond. Consequently, all statements about the ``decoherence parameter'' ζinferred from experimental data are basis-dependent as well. We illustrate this point by estimating the value of ζfor the two bases {K_L, K_S} and {K^0, \bar{K}^0} with the help of recent data of the CPLEAR experiment.
Considering semileptonic decays of the entangled B^0 \bar B^0 state which is generated in the decay of Upsilon(4S), we simply multiply the quantum-mechanical interference term by a factor (1-ζ) and use the ``decoherence parameter'' ζas a measure for deviations from quantum mechanics. We investigate several consequences of this modification of semileptonic B^0 \bar B^0 decays. In particular, we show that when confronted with the experimental values of the ratio R=(# like-sign dilepton events)/(# opposite-sign dilepton events) and of the B_H--B_L mass difference, the ensuing one standard deviation range of the decoherence parameter depends strongly on the basis in the B^0--\bar B^0 space used to build the entangled B^0 \bar B^0 state. On the other hand, in quantum mechanics physical quantities are, of course, independent of such arbitrary basis choices.
We analyze the generalized point-splitting method and Jo's result for the commutator anomaly. We find that certain classes of general regularization kernels satisfying integral conditions provide a unique result, which, however differs from Faddeev's cohomological result.
We argue that the B^0 B^0 bar state generated in the decay of Upsilon(4S) is well suited for performing tests of Einstein-Podolsky-Rosen correlations, i.e., quantum-mechanical interference effects over macroscopic distances. Using measurements of the ratio R = (#like-sign dilepton events)/(#opposite-sign dilepton events) and of the B_H - B_L mass difference we show that already presently existing data strongly favour the contribution of the interference term to R, as it is required by the rules of quantum mechanics.
We present two different aspects of the anomalies in quantum field theory. One is the dispersion relation aspect, the other is differential geometry where we derive the Stora--Zumino chain of descent equations.